Finite Group Databasebeta

← #11775229

Subgroups — #11775229

Order 1152.

441 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 441 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63486C211yesmaximal, characteristic
2C9×#407C211yesmaximal, characteristic
3C4×#3676C211yesmaximal, characteristic
4#10588144C214yesmaximal, complemented
5#69980—31nomaximal
6C23×C4×C9C2211yescharacteristic
7C22×Dic18C411yescharacteristic, complemented
8C2×C9×M16—21no—
9C2×#3676—21no—
10C2×#3676—21no—
11C2×C4⋊Dic9C411yescharacteristic, complemented
12#63486—21no—
13#63486—21no—
14#63486C412yescomplemented
15#63486C2212yes—
16C2×Dic9⋊C4—21no—
17C2×C4×Dic9—21no—
18C9×C22⋊C8—21no—
19C9×C22⋊C8C2212yes—
20C9⋊#95C2212yes—
21C2×#924—31no—
22C3×#407D311yescharacteristic
23C4×#217—31no—
24#4467—34no—
25C24×C9D411yescharacteristic
26C22×C4×C9—42no—
27C22×C4×C9C2×C411yescharacteristic
28C22×C4×C9C2×C411yescharacteristic
29C22×C4×C9D411yescharacteristic
30C22×C4×C9D411yescharacteristic
31C22×C4×C9D411yescharacteristic
32C22×C4×C9C2311yescharacteristic
33C22×Dic9—21no—
34C22×Dic9—21no—
35C22×Dic9—22no—
36C2×Dic18—21no—
37C2×Dic18—42no—
38C2×Dic18C2×C412yes—
39C9×M16—42no—
40C2×C8×C9—22no—
41#3676—24no—
42#3676—22no—
43#3676—22no—
44C4⋊Dic9—21no—
45C4⋊Dic9C2×C412yes—
46Dic9⋊C4—22no—
47Dic9⋊C4—22no—
48C4×Dic9—42no—
49#1508—91noSylow
50C23×C3×C4C2×D311yescharacteristic
51C22×Dic6—31no—
52C2×C3×M16—21no—
53C2×#217—61no—
54C2×#217—61no—
55C2×C4⋊Dic3—31no—
56#924—32no—
57#924—32no—
58#924—61no—
59#924—61no—
60C2×Dic3⋊C4—61no—
61C2×C4×Dic3—61no—
62C3×C22⋊C8—21no—
63C3×C22⋊C8C2×D312yes—
64C3⋊#95—32no—
65C23×C9—22no—
66C23×C9—22no—
67C23×C9—41no—
68C23×C9C22⋊C411yescharacteristic
69C23×C9C22⋊C411yescharacteristic
70C23×C9C2×D411yescharacteristic
71C2×C4×C9—22no—
72C2×C4×C9—22no—
73C2×C4×C9—22no—
74C2×C4×C9—41no—
75C2×C4×C9—41no—
76C2×C4×C9—41no—
77C2×C4×C9C22⋊C411yescharacteristic
78C2×C4×C9C22⋊C411yescharacteristic
79C2×C4×C9C22×C411yescharacteristic
80C2×C4×C9C2×D411yescharacteristic
81C2×Dic9—24no—
82C2×Dic9—22no—
83C2×Dic9—22no—
84C2×Dic9—42no—
85C2×Dic9—42no—
86C2×Dic9—42no—
87C2×Dic9—42no—
88Dic18—42no—
89Dic18—42no—
90C8×C9—42no—
91C2×C22⋊Q8—91no—
92#407D911yescharacteristic
93C4×C22⋊C4—91no—
94#328—94no—
95C24×C3D1211yescharacteristic
96C22×C3×C4—42no—
97C22×C3×C4C4×D311yescharacteristic
98C22×C3×C4C4×D311yescharacteristic
99C22×C3×C4D1211yescharacteristic
100C22×C3×C4#6711yescharacteristic
101C22×C3×C4#6711yescharacteristic
102C22×C3×C4C22×D311yescharacteristic
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—62no—
106C2×Dic6—32no—
107C2×Dic6—61no—
108C2×Dic6—122no—
109C3×M16—42no—
110C2×C3×C8—22no—
111#217—64no—
112#217—62no—
113#217—62no—
114C4⋊Dic3—32no—
115C4⋊Dic3—61no—
116Dic3⋊C4—62no—
117Dic3⋊C4—62no—
118C4×Dic3—122no—
119C22×C9—21no—
120C22×C9—21no—
121C22×C9—21no—
122C22×C9—21no—
123C22×C9—21no—
124C22×C9—21no—
125C22×C9—21no—
126C22×C9—44no—
127C22×C9#10412yes—
128C22×C9C2×C22⋊C411yescharacteristic
129C22×C9#13712yes—
130C4×C9—21no—
131C4×C9—21no—
132C4×C9—21no—
133C4×C9#9912yes—
134Dic9—44no—
135Dic9—42no—
136Dic9—42no—
137C22×Q8—91no—
138C23×C4C2×D911yescharacteristic
139C2×M16—21no—
140C22⋊Q8—92no—
141C22⋊Q8—92no—
142C22⋊Q8—181no—
143C22⋊Q8—181no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—181no—
146C2×C22⋊C4—181no—
147C2×C22⋊C4—181no—
148C2×C42—181no—
149C22⋊C8—21no—
150C22⋊C8C2×D912yes—
151#95—92no—
152C23×C3—22no—
153C23×C3—22no—
154C23×C3—41no—
155C23×C3(C2×D3)⋊C411yescharacteristic
156C23×C3(C2×D3)⋊C411yescharacteristic
157C23×C3C2×D1211yescharacteristic
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—41no—
162C2×C3×C4—41no—
163C2×C3×C4—41no—
164C2×C3×C4(C2×D3)⋊C411yescharacteristic
165C2×C3×C4(C2×D3)⋊C411yescharacteristic
166C2×C3×C4C2×C4×D311yescharacteristic
167C2×C3×C4C2×#6711yescharacteristic
168C2×Dic3—64no—
169C2×Dic3—62no—
170C2×Dic3—62no—
171C2×Dic3—122no—
172C2×Dic3—122no—
173C2×Dic3—122no—
174C2×Dic3—122no—
175Dic6—122no—
176Dic6—122no—
177C3×C8—42no—
178C2×C9—22no—
179C2×C9—22no—
180C2×C9—41no—
181C2×C9C2×#9911yescharacteristic
182C2×C9#41911yescharacteristic
183C2×C9C2×#10411yescharacteristic
184C24D3611yescharacteristic
185C2×Q8—92no—
186C2×Q8—181no—
187C2×Q8—362no—
188C22×C4—42no—
189C22×C4—181no—
190C22×C4—181no—
191C22×C4—182no—
192C22×C4C4×D911yescharacteristic
193C22×C4C4×D911yescharacteristic
194C22×C4D3611yescharacteristic
195C22×C4#61111yescharacteristic
196C22×C4#61111yescharacteristic
197C22×C4C22×D911yescharacteristic
198M16—42no—
199C2×C8—22no—
200C4⋊C4—92no—
201C4⋊C4—181no—
202C4⋊C4—182no—
203C4⋊C4—182no—
204C22⋊C4—184no—
205C22⋊C4—182no—
206C22⋊C4—182no—
207C42—362no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—44no—
216C22×C3#82512yes—
217C22×C3#90912yes—
218C22×C3C2×(C2×D3)⋊C411yescharacteristic
219C3×C4—21no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4#80612yes—
223Dic3—124no—
224Dic3—122no—
225Dic3—122no—
226C9#150811yescharacteristic, complemented, Sylow
227C23—22no—
228C23—22no—
229C23—41no—
230C23(C2×D9)⋊C411yescharacteristic
231C23(C2×D9)⋊C411yescharacteristic
232C23C2×D3611yescharacteristic
233Q8—362no—
234Q8—362no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—184no—
242C2×C4—182no—
243C2×C4—182no—
244C2×C4—362no—
245C2×C4—362no—
246C2×C4—362no—
247C2×C4—362no—
248C2×C4(C2×D9)⋊C411yescharacteristic
249C2×C4(C2×D9)⋊C411yescharacteristic
250C2×C4C2×C4×D911yescharacteristic
251C2×C4C2×#61111yescharacteristic
252C8—42no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—41no—
256C2×C3C2×#80611yescharacteristic
257C2×C3#512011yescharacteristic
258C2×C3C2×#82511yescharacteristic
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22#6338412yes—
268C22#6347112yes—
269C22C2×(C2×D9)⋊C411yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—364no—
274C4—362no—
275C4—362no—
276C4#6336512yes—
277C3#6998011yescharacteristic
278C2—22no—
279C2—22no—
280C2—41no—
281C2C2×#6336511yescharacteristic
282C2#1058880411yescharacteristic
283C2C2×#6338411yescharacteristic
subgroupG/H
centerC22C2×(C2×D9)⋊C4
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#407C2
socleC22×C3C2×(C2×D3)⋊C4
prime radicalC24×C3D12
cosocleC22×C4×C9C23
hypercenter#407D9
hypocenterC9#1508
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #10588144C2semidirect
7. C22×Dic18C4semidirect
11. C2×C4⋊Dic9C4semidirect
14. #63486C4semidirect
226. C9#1508semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#634862
C9×#4072
C4×#36762
#105881442
#699803